Compact lifting conjecture for discriminant-preserving symmetries

Let $f$ be the multigerm under consideration, let $p:\mathcal{A}_f\to\widetilde{\operatorname{Inv}}(D(f))$ be the target-action homomorphism, and let $H_0$ be a compact linear subgroup of $\tilde{\operatorname{Inv}}(D(f_0))$, where $f_0$ is the finitely determined representative used in the preceding argument. Compact lifting conjecture. There exists a compact subgroup $\tilde{G}$ of $\mathcal{A}_f$ such that

$$p(\tilde{G})\supset H_0.$$

The conjecture asks whether the arbitrarily accurate jet-level liftings constructed in the preceding proposition can be realized by an actual compact subgroup at the map-germ level. The source says that this will be considered in a forthcoming paper; no resolution is supplied here.